Analytical Theory of Turbulent Diffusion
Analytical Theory of Turbulent Diffusion
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J»«l. _ where \|r (x, t) = ijf (x, t|x, 0) and \|f (y, s) = \|/p(y^s|y, 0) denote the unaveraged Green's functions. In stationary homogeneous flows, this result reduces to (3-21) on the assimption that the )jf and u fields are uncorrelated (cf. Sec. Aw 2. 5). 27. Also, by adding to (5. 19) to the analagous equation for the deri- vative with respect to s, and setting t = s, ve find It = / ^^(;::'^^^i. V°)^iY^ = = ij- / dt' / dx'U, . (xSt')G(x', t') 2 / df / drU. . (r +r, t-t') R(r, t, t'lr, 0)+R...(r, f, t|r, 0) (3. 22) For t « T(r ), R is negligible except near r = 0, and the right-hand side of O MM (5. 22) becomes U. . (0, 0) - U. . (r, 0) t, in agreement with (3. 10). For t » l/v, R is appreciable even at for sepa- rations r of order I. For such large separations, the second term on the right-hand side of (3-22) is quite negligible, and we find (cf. Eqs. 2. 27, ^. 28) =2 =2 =kK (3. 25) This is consistent with the intuitive notion that, at such large separations from their source and each other, the particles will wander independently as 28.
What to read after Analytical Theory of Turbulent Diffusion?
You can find similar books in the "Read Also" column, or choose other free books by P H Roberts to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
J»«l. _ where \|r (x, t) = ijf (x, t|x, 0) and \|f (y, s) = \|/p(y^s|y, 0) denote the unaveraged Green's functions. In stationary homogeneous flows, this result reduces to (3-21) on the assimption that the )jf and u fields are uncorrelated (cf. Sec. Aw 2. 5). 27. Also, by adding to (5. 19) to the analagous equation for the deri- vative with respect to s, and setting t = s, ve find It = / ^^(;::'^^^i. V°)^iY^ = = ij- / dt' / dx'U, . (xSt')G(x', t') 2 / df / drU. . (r +r, t-t') R(r, t, t'lr, 0)+R...(r, f, t|r, 0) (3. 22) For t « T(r ), R is negligible except near r = 0, and the right-hand side of O MM (5. 22) becomes U. . (0, 0) - U. . (r, 0) t, in agreement with (3. 10). For t » l/v, R is appreciable even at for sepa- rations r of order I. For such large separations, the second term on the right-hand side of (3-22) is quite negligible, and we find (cf. Eqs. 2. 27, ^. 28) =2 =2 =kK (3. 25) This is consistent with the intuitive notion that, at such large separations from their source and each other, the particles will wander independently as 28.
What to read after Analytical Theory of Turbulent Diffusion?
You can find similar books in the "Read Also" column, or choose other free books by P H Roberts to read onlineMoreLess
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